Yongmei M. Jin

Nanoscale phase field microelasticity theory of dislocations: model and 3D simulations

The first Phase Field model of evolution of a multi-dislocation system in elastically anisotropic crystal under applied stress is formulated. The model is a modification and extension of our Phase Field Microelasticity approach to the theory of coherent phase transformations. The long-range strain-induced interaction of individual dislocations is calculated exactly and is explicitly incorporated in the Phase Field formalism. It also automatically takes into account the effects of “short-range interactions”, such as multiplication and annihilation of dislocations and a formation of various metastable microstructures involving dislocations and defects. The proposed 3-dimensional Phase Field model of dislocations does not impose a priori constraints on possible dislocation structures or their evolution paths. Examples of simulation of the FCC 3D system under applied stress are considered.

Three-dimensional phase field model of proper martensitic transformation

Abstract The Phase Field Microelasticity theory is developed for proper multivariant martensitic transformations. The model is based on the exact solution of the elasticity problem in the homogeneous modulus approximation. The model takes into account the transformation-induced coherency strain and provides for the strain compatibility throughout the system. Computer simulations are performed for a dilatationless cubic→tetragonal martensitic transformation and for the transformation with parameters corresponding to a martensitic transformation Fe–31%Ni alloy. The development of the martensitic transformation through nucleation, growth and coarsening of orientation variants is simulated at different levels of undercooling. The simulated martensitic structure has a complex polytwinned morphology. Simulation demonstrates that the presence of a non-zero volumetric component in the transformation strain in the Fe–31%Ni system significantly affects the martensitic transformation.

Adaptive ferroelectric states in systems with low domain wall energy: Tetragonal microdomains

Ferroelectric and ferroelastic phases with very low domain wall energies have been shown to form miniaturized microdomain structures. A theory of an adaptive ferroelectric phase has been developed to predict the microdomain-averaged crystal lattice parameters of this structurally inhomogeneous state. The theory is an extension of conventional martensite theory, applied to ferroelectric systems with very low domain wall energies. The case of ferroelectric microdomains of tetragonal symmetry is considered. It is shown for such a case that a nanoscale coherent mixture of microdomains can be interpreted as an adaptive ferroelectric phase, whose microdomain-averaged crystal lattice is monoclinic. The crystal lattice parameters of this monoclinic phase are self-adjusting parameters, which minimize the transformation stress. Self-adjustment is achieved by application of the invariant plane strain to the parent cubic lattice, and the value of the self-adjusted parameters is a linear superposition of the lattice c...

Three-dimensional phase field model of low-symmetry martensitic transformation in polycrystal: simulation of ζ′2 martensite in AuCd alloys

A three-dimensional phase field model of the martensitic transformation that produces a low symmetry phase in polycrystals is developed. The transformation-induced strain mostly responsible for the specific features of the martensitic transformation is explicitly taken into account. The high computational efficiency of the model turns out to be almost independent of the complexity of the polycrystal geometry. An example of the cubic→trigonal transformation in AuCd alloys producing ζ′2 martensite is considered. The development of the transformation through nucleation, growth and coarsening of orientation variants is simulated for both single crystal and polycrystalline materials. The effect of an external load on the martensitic microstructure in the polycrystalline material is studied. It is shown that the elastic coupling between different transformed grains of the polycrystal drastically affects the microstructure and its response to the applied stress. The obtained self-accommodating morphologies of the multivariant martensitic structure are in agreement with those observed in the experiments.

Phase field microelasticity theory and modeling of elastically and structurally inhomogeneous solid

The phase field microelasticity theory of a three-dimensional elastically anisotropic solid of arbitrarily inhomogeneous modulus also containing arbitrary structural inhomogeneities is proposed. The theory is based on the equation for the strain energy of the elastically and structurally inhomogeneous system presented as a functional of the phase field, which is the effective stress-free strain of the “equivalent” homogeneous modulus system. It is proved that the stress-free strain minimizing this functional fully determines the exact elastic equilibrium in the elastically and structurally inhomogeneous solid. The stress-free strain minimizer is obtained as a steady state solution of the time-dependent Ginzburg–Landau equation. The long-range strain-induced interaction due to the elastic and structural inhomogeneities is explicitly taken into account. Systems with voids and cracks are the special cases covered by this theory since voids and cracks are elastic inhomogeneities that have zero modulus. Other ...

Phase field microelasticity theory and modeling of multiple dislocation dynamics

The phase field theory and model of a multidislocation dynamics in an elastically anisotropic crystal under applied stress is developed. The proposed three-dimensional (3D) model is a particular case of our phase field microelasticity model of the stress-induced martensitic transformations. A spontaneous self-organization of dislocations in the evolving ensemble, which involves multiplication/annihilation and movement of dislocations controlled by their elastic interaction, is described by the Ginzburg–Landau kinetic equation. Examples of 3D computer simulation of dislocation dynamics are considered.

Three-dimensional phase field microelasticity theory and modeling of multiple cracks and voids

It is proved that the stress-free strain distribution minimizing the strain energy of the homogeneous modulus body fully determines the elasticity of the discontinuous body. This result is used as a basis for the proposed three-dimensional phase field microelasticity theory and model of a discontinuous body with cracks and voids in elastically anisotropic crystal under applied stress. The elastic equilibrium and spontaneous evolution of these defects are described by the Ginzburg–Landau kinetic equation. Examples of computations of elastic equilibrium and evolutions of systems with cracks and/or voids are considered.

Phase field microelasticity theory and simulation of multiple voids and cracks in single crystals and polycrystals under applied stress

The phase field microelasticity theory of a three-dimensional elastically anisotropic single crystal with multiple voids and cracks is developed. It is extended to the case of elastically isotropic polycrystal. The theory is based on the exact equation for the strain energy of the “equivalent” continuous elastically homogeneous body presented as a functional of the phase field. This field is the equivalent stress-free strain. It is proved that the equivalent stress-free strain minimizing the strain energy of the elastically homogeneous body fully determines the elastic strain and displacement of the body with voids/cracks. The geometry and evolution of multiple voids and cracks are described by the phase field, which is a solution of the stochastic time-dependent Ginzburg–Landau equation. Other stress-generating defects, such as dislocations and precipitates, are trivially integrated into this theory. The proposed model does not impose a priori constraints on the configuration of multiple voids and cracks...

Phase field microelasticity modeling of dislocation dynamics near free surface and in heteroepitaxial thin films

Abstract Dislocation dynamics near a free surface and in heteroepitaxial thin films are simulated using an extended version of the nanoscale Phase Field Microelasticity model of dislocations [Acta Mater. 49 (2001) 1847]. The model automatically takes into account the effect of image forces on dislocation motions. In particular, the operations of Frank–Read sources in epitaxial films grown on infinitely thick and relatively thin substrates are investigated. The simulation reveals different misfit dislocation behaviors at the interface. Its implication on the interface susceptibility to crack nucleation is discussed.

Magnetic structure and hysteresis in hard magnetic nanocrystalline film: Computer simulation

Three-dimensional micromagnetic simulations are used to study the effect of crystallographic textures on the magnetic properties of uniaxial nanocrystalline films of hard magnetic materials with arbitrary grain shapes and size distributions. The correlation lengths (effective ferromagnetic exchange interaction radius and domain wall width) are assumed to be smaller than the typical grain size. The Landau–Lifshitz equations of magnetization dynamics are employed to describe the distribution of magnetization in ferromagnetic domains, domain evolution during magnetization switching, and the hysteresis curve. The equations are solved numerically in reciprocal space using the fast Fourier transform technique. Simulations are performed for films of different grain textures. The results show that magnetic coupling between grains in thin films significantly affects the morphology of the magnetic domains and their response to the magnetic field applied. The greater the deviation of the uniaxial directions of the g...